Diffraction of sound around corners and over wide barriers

Abstract

Formulas and procedures are described for the estimation of sound pressure amplitudes at locations partially shielded from the source by a barrier. The analytical development is based on the idealized models of a wave from a point or extended source incident on a rigid wedge or a three-sided semi-infinite barrier. Versions of the uniform asymptotic solution for the wedge problem which are convenient for numerical predictions are derived in terms of auxiliary Fresnel functions by means of complex variable techniques previously employed by Pauli from a generalization of the exact integral solution developed by Sommerfeld, MacDonald, Bromwich, and others and are interpreted within the spirit of Keller's geometrical theory of diffraction. The Kirchhoff approximation in terms of the Fresnel number is obtained in the limit of small angular deflections from shadow zone boundaries. An approximate and relatively simple expression for the double-edge diffraction by a thick three-sided barrier is given based on the single wedge diffraction solution and on concepts inherent to the geometrical theory of diffraction which reduces to finite and realistic limits when either source or listener are near the extended plane of the barrier's top. A simple approximation suggested by Maekawa based on the replacement of actual barriers by an equivalent thin screen with diffraction treated by the Kirchhoff approximation is discussed in terms of the present theory and it is concluded that in some instances this approximation may lead to sizeable errors. An alternate scheme is suggested whereby one approximates the actual barrier by a three-sided barrier wholly contained within the actual barrier.

Urban Background Noise Mapping: The General Model

“…In a first step, ground reflection is ignored. According to the literature [21,22,23,24], A bar,f lat,0 can be expressed with high accuracy by equation (4):…”

“…Definitions of parameters are shown in figure 2. f (Y ) and g(Y ) are functions of Fresnel integrals C and S [21]:…”

Sound barriers to enable open windows and integration in landscape

“…Tolstoy [2] obtained an exact explicit solution for the sound diffracted by a wedge, represented by a sum of infinite series. For a review of other solution methods, see Maekawa [3], Pierce [4], Hu and Wong [5], Menounou et al [6], Menounou [7], Quis [8], Li and Wong [9], among many others.…”

A Scale Model Study of Parallel Urban Canyons

“…The source was positioned at ( Figure 6 shows a comparison of a calculation with a finite barrier, calculated by a time domain formulation by Svensson [44] and an infinite barrier calculated with the model of Pierce [43]. The receiver is in the shadow zone of the barrier and horizontal diffraction around the barrier has not been included.…”

“…The method does however have the advantage over the former methods that the time-frequency resolution varies with frequency and is generated implicitly with the method (no choices of filter or window widths have to be made). Infinitely long screen calculation [43], Circles: 100 m long screen calculation [44]. …”